Grading Entropy Variation Due to Soil Crushing

The grading entropy of a soil $\left(S\right)$ is derived in terms of the more general concept of statistical entropy. It consists of two terms: the base entropy $\left(S_0\right)$ , arising from the difference in the width of the statistical cells in the conventional grading curve, and the entropy increment $\left(\Delta S\right)$ . The goal of the research was to study which grading entropy plays the role of the “true” entropy in a thermodynamic sense (i.e., undergoes an increase during the crushing process being considered as an irreversible thermodynamic process): the entropy increment $\left(\Delta S\right)$ or the sum of the base entropy and the entropy increment $\left(S\right)$ . The soil samples were subjected to successive crushing treatments; the grading curve and the grading entropy were determined after each treatment. It was found that only the entropy increment $\left(\Delta S\right)$ increased monotonically with an increasing number of crushing treatments. Therefore, the ultimate state can be expected to be characterized by maximum entropy increment $\left(\Delta S\right)$ and, by such grading curve where the relative frequencies of the fractions are equal.